Question
Write the equation in its equivalent exponential form. 10) \( \log _{6} 216=x \)
Ask by Harper Park. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(6^{x} = 216\)
Solution
To convert the logarithmic equation \(\log _{6} 216 = x\) into its equivalent exponential form, you can use the definition of logarithms:
\[
\log_{b} a = c \quad \text{is equivalent to} \quad b^c = a
\]
Applying this to your equation:
\[
\log_{6} 216 = x \quad \Longleftrightarrow \quad 6^{x} = 216
\]
**Final Answer:**
\[
6^{x} = 216
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To convert the logarithmic equation \( \log_{6} 216 = x \) into exponential form, you can rewrite it as \( 6^x = 216 \). This means that 6 raised to the power of \( x \) equals 216. So, if you find the value of \( x \), you'll be discovering the exponent necessary to reach 216 when starting from 6! Now, if you delve into the actual numbers, you'll find that 216 can be expressed as \( 6^3 \). So, \( x = 3 \). What a neat little discovery, right? You've just transformed a log into a power!
